Mathematical Statistics with Applications, Seventh Edition

www.downloadslide.com

www.downloadslide.com Exercises 403 8.22 An increase in the rate of consumer savings frequently is tied to a lack of confidence in the economy and is said to be an indicator of a recessional tendency in the economy. A random sampling of n = 200 savings accounts in a local community showed the mean increase in savings account values to be 7.2% over the past 12 months, with standard deviation 5.6%. Estimate the mean percentage increase in savings account values over the past 12 months for depositors in the community. Place a bound on your error of estimation. 8.23 The Environmental Protection Agency and the University of Florida recently cooperated in a large study of the possible effects of trace elements in drinking water on kidney-stone disease. The accompanying table presents data on age, amount of calcium in home drinking water (measured in parts per million), and smoking activity. These data were obtained from individuals with recurrent kidney-stone problems, all of whom lived in the Carolinas and the Rocky Mountain states. Carolinas Rockies Sample size 467 191 Mean age 45.1 46.4 Standard deviation of age 10.2 9.8 Mean calcium component (ppm) 11.3 40.1 Standard deviation of calcium 16.6 28.4 Proportion now smoking .78 .61 a b c Estimate the average calcium concentration in drinking water for kidney-stone patients in the Carolinas. Place a bound on the error of estimation. Estimate the difference in mean ages for kidney-stone patients in the Carolinas and in the Rockies. Place a bound on the error of estimation. Estimate and place a 2-standard-deviation bound on the difference in proportions of kidney-stone patients from the Carolinas and Rockies who were smokers at the time of the study. Text not available due to copyright restrictions 8.25 A study was conducted to compare the mean number of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The sample statistics are given in the following table. Region 1 2 Sample size 100 100 Sample mean 2.4 3.1 Sample variance 1.44 2.64 Text not available due to copyright restrictions

www.downloadslide.com 404 Chapter 8 Estimation a b Estimate the difference in the mean number of police emergency calls per 8-hour shift between the two districts in the city. Find a bound for the error of estimation. 8.26 The Mars twin rovers, Spirit and Opportunity, which roamed the surface of Mars in the winter of 2004, found evidence that there was once water on Mars, raising the possibility that there was once life on the plant. Do you think that the United States should pursue a program to send humans to Mars? An opinion poll 3 indicated that 49% of the 1093 adults surveyed think that we should pursue such a program. a b Estimate the proportion of all Americans who think that the United States should pursue a program to send humans to Mars. Find a bound on the error of estimation. The poll actually asked several questions. If we wanted to report an error of estimation that would be valid for all of the questions on the poll, what value should we use? [Hint: What is the maximum possible value for p × q?] 8.27 A random sample of 985 “likely voters”—those who are judged to be likely to vote in an upcoming election—were polled during a phone-athon conducted by the Republican Party. Of those contacted, 592 indicated that they intended to vote for the Republican running in the election. a b c According to this study, the estimate for p, the proportion of all “likely voters” who will vote for the Republican candidate, is p = .601. Find a bound for the error of estimation. If the “likely voters” are representative of those who will actually vote, do you think that the Republican candidate will be elected? Why? How confident are you in your decision? Can you think of reasons that those polled might not be representative of those who actually vote in the election? 8.28 In a study of the relationship between birth order and college success, an investigator found that 126 in a sample of 180 college graduates were firstborn or only children; in a sample of 100 nongraduates of comparable age and socioeconomic background, the number of firstborn or only children was 54. Estimate the difference in the proportions of firstborn or only children for the two populations from which these samples were drawn. Give a bound for the error of estimation. 8.29 Sometimes surveys provide interesting information about issues that did not seem to be the focus of survey initially. Results from two CNN/USA Today/Gallup polls, one conducted in March 2003 and one in November 2003, were recently presented online. 4 Both polls involved samples of 1001 adults, aged 18 years and older. In the March sample, 45% of those sampled claimed to be fans of professional baseball whereas 51% of those polled in November claimed to be fans. a b Give a point estimate for the difference in the proportions of Americans who claim to be baseball fans in March (at the beginning of the season) and November (after the World Series). Provide a bound for the error of estimation. Is there sufficient evidence to conclude that fan support is greater at the end of the season? Explain. 3. Source: “Space Exploration,” Associated Press Poll, http:www.pollingreport.com/science.htm#Space, 5 April 2004. 4. Source: Mark Gillespie,“Baseball Fans Overwhelmingly Want Mandatory Steroid Testing,” http:www. gallup.com/content/print/.aspx?ci=11245, 14 February 2004.